A086368 Nonsquarefree numbers k such that sigma(k) is squarefree.

4, 8, 9, 16, 18, 20, 25, 36, 45, 49, 50, 64, 72, 80, 100, 104, 116, 117, 121, 128, 144, 148, 169, 180, 196, 200, 208, 225, 234, 242, 244, 256, 261, 289, 292, 296, 320, 325, 333, 361, 369, 404, 436, 441, 450, 452, 464, 488, 512, 529, 548, 549, 576, 578, 584, 592

Offset: 1

Author

Labos Elemer, Sep 05 2003

Keywords

• nonn

Examples

			k = 45 = 3*3*5 and sigma(45) = 78 = 2*3*13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A065300.

Cf. A000203 (sigma), A005117, A065303, A087249, A065301.

Programs

Maple

filter:= n -> not numtheory:-issqrfree(n) and numtheory:-issqrfree(numtheory:-sigma(n)):
select(filter, [$1..1000]); # Robert Israel, May 11 2018

Mathematica

q[k_] := ! SquareFreeQ[k] && SquareFreeQ[DivisorSigma[1, k]]; Select[Range[600], q] (* Amiram Eldar, Feb 24 2025 *)

PARI

isok(k) = !issquarefree(k) && issquarefree(sigma(k)); \\ Amiram Eldar, Feb 24 2025